She also thanked Craig Foster, a TV host and former Australian national football captain who rallied the international football community, and sports bodies including Fifa and the International Olympic Committee to help secure a release.
Mr Foster, who escorted al-Araibi on his arrival, said the human rights victory marked “the beginning of a broader fight for the values of sport”.
“We fought for one soul because Hakeem represented everyone who suffers under tyranny,” he said in a statement.
The footballer plays for Melbourne team Pascoe Vale FC. Many of the team’s members were at the airport on Tuesday.
‘You’ll Never Walk Alone’
Hywel Griffith, BBC News in Melbourne
As he walked out of the airport arrival gates, Hakeem al-Araibi seemed astounded by the welcoming party that had gathered to greet him.
Some supporters had banners and posters baring his picture, others wore T-shirts with the campaign slogan #SaveHakeem.
They cheered as if greeting a cup-winning captain and sang one of football’s most poignant anthems, You’ll Never Walk Alone.
His case has shown the solidarity that exists across the game, as players and fans lobbied for his return.
But the apparent delay by Fifa in becoming involved has left the game’s governing body open to accusations of neglect and failing to stand by its own policy on human rights.